Try holding a cloth or flanel over the overflow then use a plunger on the plug hole. Or if you havent got a plunger then use with another cloth/flanel to swiftly pump up & down to relase the blockage.
we had this recently and I tried a plunger, a metal coat hanger (opened up), and a long stick, none of which worked, in the end Mr Jules had to undo the U bend and empty the waste into a bucket .
soda crystals are very good, they are cheap too(about 50p a packet) you just pour them down and put a kettle full of boiling water down. you can get them from most supermarkets.
I was able to use a pressure washer in the kitchen sink in my last house - put the nozzle down the plughole and wrap an old cloth round it to prevent any splash back and rember to cover the over flow as well and let rip.